Tilt compensation, measurement, and associated adjustment of refractive prescriptions during surgical and other treatments of the eye

ABSTRACT

Embodiments of the present invention provide methods and systems for determining an ablation treatment for an eye of a patient. The systems and method may involve determining an ellipsoid shape corresponding to an anterior corneal surface of the patient&#39;s eye. The ellipsoid shape may include an anterior portion, a major axis, and an apex, where the major axis intersects the anterior portion at the apex. The systems and method may also involve determining a tilted orientation of the eye, such as when the patient fixates on a target during a laser ablation procedure. The systems and method may further involve determining the ablation treatment based on the ellipsoid shape and/or the tilted orientation.

BACKGROUND OF THE INVENTION

Embodiments of the present invention are generally related todetermining ablation treatments for laser eye treatment surgery. Theinvention provides systems and methods for determining ablationtreatments based on a tilted orientation of a patient's eye.

Known laser eye surgery procedures generally employ an ultraviolet orinfrared laser to remove a microscopic layer of stromal tissue from thecornea of the eye. Examples of laser eye surgery procedures includephotorefractive keratectomy (PRK), phototherapeutic keratectomy (PTK),laser assisted in situ keratomileusis (LASIK), laser epithelialkeratomileusis (LASEK), and the like. A laser typically removes aselected shape of a corneal tissue, often to correct refractive errorsof an eye. Ultraviolet laser ablation results in photodecomposition of acorneal tissue, but generally does not cause significant thermal damageto adjacent and underlying tissues of an eye. Irradiated molecules arebroken into smaller volatile fragments photochemically, directlybreaking intermolecular bonds.

Laser ablation procedures can remove a targeted amount stroma of acornea to change a cornea's contour for varying purposes, such as forcorrecting myopia, hyperopia, astigmatism, and the like. Control over adistribution of ablation energy across a cornea may be provided by avariety of systems and methods, including use of ablatable masks, fixedand moveable apertures, controlled scanning systems, eye movementtracking mechanisms, and the like. In known systems, a laser beam oftencomprises a series of discrete pulses of laser light energy, with atotal shape and amount of tissue removed being determined by a shape,size, location, and/or number of laser energy pulses impinging on acornea. A variety of algorithms may be used to calculate the pattern oflaser pulses used to reshape a cornea so as to correct a refractiveerror of an eye.

Known systems make use of a variety of forms of lasers and laser energyto effect a correction, including infrared lasers, ultraviolet lasers,femtosecond lasers, wavelength multiplied solid-state lasers, and thelike. Alternative vision correction techniques make use of radialincisions in a cornea, intraocular lenses, removable corneal supportstructures, and the like.

Known corneal correction treatment methods have generally beensuccessful in correcting standard vision errors, such as myopia,hyperopia, astigmatism, and the like. By customizing an ablation patternbased on wavefront measurements, it may be possible to correct minoraberrations so as to reliably and repeatedly provide visual acuitygreater than 20/20. Such detailed corrections will benefit from anextremely accurate ablation of tissue.

Known methods for calculation of a customized ablation pattern usingwavefront sensor data generally involves mathematically modeling asurface of the cornea using expansion series techniques. Morespecifically, Zernike polynomials have been employed to model thecorneal surface and refractive aberrations of the eye. Coefficients of aZernike polynomial are derived through known fitting techniques, and anoptical correction procedure is then determined using a shape indicatedby a mathematical series expansion model.

Known methodology for determining laser ablation treatments based onwavefront sensor data and spectacles often provides real benefits topatients in need thereof. Yet further advancement in ablation techniquetechnology, particularly for refractive correction purposes, is desired.Embodiments of the present invention provide solutions for at least someof these outstanding needs.

BRIEF SUMMARY OF THE INVENTION

Embodiments of the present invention provide systems and methods forvision treatment which take into account a detailed ablative interactionof a laser beam with a detailed anatomy of a tissue surface of an eye.Exemplary techniques may involve determining an ellipsoid shapecorresponding to an anterior corneal surface of the patient's eye. Theellipsoid shape may include an anterior portion, a major axis, and anapex, where the major axis intersects the anterior portion at the apex.The systems and method may also involve determining a tilted orientationof the eye, such as when the patient fixates on a target during a laserablation procedure. The systems and method may further involvedetermining the ablation treatment based on the ellipsoid shape and/orthe tilted orientation.

In one aspect, embodiments of the present invention may include a methodfor determining an ablation treatment for an eye of a patient. Themethod may include determining an ellipsoid shape corresponding to ananterior corneal surface of the eye, the ellipsoid shape having ananterior portion, a major axis, and an apex such that the major axisintersects the anterior portion at the apex. The method may also includedetermining a tilted orientation of the eye when the patient fixates ona target during a laser ablation procedure and determining the ablationtreatment based on the ellipsoid shape and the tilted orientation.

The tilted orientation may include the major axis rotationally offsetfrom an axis of a laser beam path. In one embodiment, determining thetilted orientation may include determining a vertex of the ellipsoidwhere the vertex corresponds to a foremost point of the anterior cornealsurface, and determining an offset between the apex and the vertex. Inanother embodiment, determining the tilted orientation may includeobtaining a topography measurement of the anterior corneal surface andfitting the topography measurement on the ellipsoid shape to obtain thetilted orientation. In another embodiment, determining the ellipsoidshape may include determining a keratometry profile of the anteriorcorneal surface. The keratometry profile may include a first curvaturevalue, a second curvature value, and a torsional rotational angle.

The tilted orientation may include a first tilt in a first direction anda second tilt in a second direction orthogonal to the first direction.The method may further include determining an energy level for a lasertreatment device based on the ablation treatment and/or an ablation timefor the laser treatment device based on the ablation treatment.

In another aspect, embodiments of the present invention may include amethod for determining an ablation treatment for an eye of a patient.The method may include determining an ellipsoid model corresponding toan anterior corneal surface of the eye, the ellipsoid model having ananterior portion, a major axis, and an apex such that the major axisintersects the anterior portion at the apex. The method may also includecalculating a nominal ablation pattern for the eye based on theellipsoid model. The method may further include determining a tiltedorientation of the eye when the patient fixates on a target during alaser ablation procedure; where determining the tilted orientationincludes: determining a surface slope of the anterior corneal surface ina first direction extending radially from the apex; determining asurface slope of the anterior corneal surface in a second directionextending radially from the apex, where the surface slope in the firstdirection is steeper than the surface slope in the second direction; anddetermining the ablation treatment by adjusting the nominal ablationpattern based on the surface slope in the first direction and thesurface slope in the second direction.

The nominal ablation pattern may be based on a surface slope of anon-tilted ellipsoid model. Determining the nominal ablation pattern mayinclude calculating a cosine adjustment measure based on a non-tiltedellipsoid model and determining the ablation pattern may includeadjusting the cosine adjustment measure based on an adjusted surfaceslope corresponding to the tilted orientation. Calculating the nominalablation pattern may include applying a cosine adjustment measure to awavefront guided treatment plan and adjusting the nominal ablationpattern may include adjusting the cosine adjustment measure based on thetilted orientation.

The method may additionally include determining a misalignment betweenan axis of a laser beam and a vertex of the ellipsoid model where thevertex corresponds to a foremost point of the anterior corneal surface,and adjusting the ablation pattern based on the misalignment.

In another aspect, embodiments of the present invention may include acomputer program product for determining an ablation treatment for aneye of a patient. The program product may include code for accepting anellipsoid shape corresponding to an anterior corneal surface of the eyewhere the ellipsoid shape has an anterior portion, a major axis, and anapex such that the major axis intersects the anterior portion at theapex. The program product may also include code for accepting a tiltedorientation of the eye where the tilted orientation corresponds to alaser ablation procedure target fixation of the patient's eye. Theprogram product may further include code for determining the ablationtreatment based on the ellipsoid shape and the tilted orientation and acomputer-readable medium for storing the codes.

In another aspect, embodiments of the present invention may include amachine-readable medium having machine-executable instructionsconfigured to perform a method for determining an ablation treatment foran eye of a patient where the includes determining an ellipsoid shapecorresponding to an anterior corneal surface of the eye, the ellipsoidshape having an anterior portion, a major axis, and an apex such thatthe major axis intersects the anterior portion at the apex. The methodmay also include determining a tilted orientation of the eye when thepatient fixates on a target during a laser ablation procedure anddetermining the ablation treatment based on the ellipsoid shape and thetilted orientation.

The method may further include determining a misalignment between theaxis of the laser beam and a vertex of the ellipsoid shape where thevertex corresponds to a foremost point of the anterior corneal surface,and may include adjusting the laser ablation pattern based on themisalignment. The method may additionally include determining an energylevel for a laser treatment device based on the laser ablation patternand/or determining an ablation time for the laser treatment device basedon the laser ablation pattern. In some embodiments, the tiltedorientation may include the major axis rotationally offset from an axisof a laser beam path.

In another aspect, embodiments of the present invention may include asystem for determining an ablation treatment for an eye of a patient.The system may include a first input module comprising a tangible mediumembodying machine-readable code that receives an ellipsoid shapecorresponding to an anterior corneal surface of the eye where theellipsoid shape includes an anterior portion, a major axis, and an apexsuch that the major axis intersects the anterior portion at the apex.The system may also include a second input module comprising a tangiblemedium embodying machine-readable code that receives a tiltedorientation of the eye where the tilted orientation corresponds to alaser ablation procedure target fixation of the patient's eye. Thesystem may further include a treatment module comprising a tangiblemedium embodying machine-readable code that that determines the ablationtreatment based on the ellipsoid shape and the tilted orientation.

In another aspect, embodiments of the present invention may include asystem for determining an ablation treatment for an eye of a patient.The system may include a laser ablation device that emits a laser beamto ablate at least a portion of the cornea of the patient's eye and acontrol device communicatively coupled with the laser ablation deviceand configured to control the laser ablation device according to theablation treatment. The ablation treatment may be determined from amethod including determining an ellipsoid shape corresponding to ananterior corneal surface of the eye where the ellipsoid shape has ananterior portion, a major axis, and an apex such that the major axisintersects the anterior portion at the apex. The method may also includedetermining a tilted orientation of the eye when the patient fixates ona target during a laser ablation procedure and determining the laserablation treatment based on the ellipsoid shape and the tiltedorientation.

The method may further include determining a misalignment between anaxis of the laser beam and a vertex of the ellipsoid shape where thevertex corresponds to a foremost point of the anterior corneal surfaceand adjusting the laser ablation pattern based on the misalignment.Adjusting the laser ablation pattern based on the misalignment mayinclude adjusting a cosine measure to account for the misalignment. Themethod may additionally include determining an energy level for thelaser ablation device based on the laser ablation pattern and/ordetermining an ablation time for the laser ablation device based on thelaser ablation pattern.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a laser ablation system according to an embodiment ofthe present invention.

FIG. 2 illustrates a simplified computer system according to anembodiment of the present invention.

FIG. 3 illustrates a wavefront measurement system according to anembodiment of the present invention.

FIG. 3A illustrates another wavefront measurement system according to anembodiment of the present invention.

FIG. 4A illustrates a two dimensional elliptical approximation of theprofile of an eye according to an embodiment of the present invention.

FIGS. 4B-C illustrate various effects the sloped corneal surface of aneye may have on a laser ablation treatment according to an embodiment ofthe present invention.

FIG. 5A illustrates a two dimensional elliptical approximation of atilted profile of an eye according to an embodiment of the presentinvention.

FIGS. 5B-C provide graphical illustrations of a cosine effect asymmetrythat may result due to a tilted orientation of an eye according to anembodiment of the present invention.

FIGS. 5D-E provide histograms of measured tilts of left and right eyesaccording to an embodiment of the present invention.

FIG. 6A provides a graphical illustration of effects that de-centeringmay have during a laser ablation treatment according to an embodiment ofthe present invention.

FIG. 6B provides a graphical illustration of a adjustment coefficientfor a de-centering shift according to an embodiment of the presentinvention.

FIG. 7 illustrates a method for determining an ablation treatment basedon a tilted orientation according to an embodiment of the presentinvention.

FIG. 8 illustrates another method for determining an ablation treatmentbased on a tilted orientation according to an embodiment of the presentinvention.

FIG. 9 illustrates another method for determining an ablation treatmentbased on a tilted orientation according to an embodiment of the presentinvention.

FIG. 10 illustrates another method for determining an ablation treatmentbased on a tilted orientation according to an embodiment of the presentinvention.

FIG. 11 illustrates another method for determining an ablation treatmentbased on a tilted orientation according to an embodiment of the presentinvention.

FIGS. 12A-D provide various graphical illustrations associated withablation treatment adjustment examples according to an embodiment of thepresent invention.

FIG. 13 illustrates another method for determining an ablation treatmentbased on a tilted orientation according to an embodiment of the presentinvention.

FIG. 14 illustrates another method for determining an ablation treatmentbased on a tilted orientation according to an embodiment of the presentinvention.

FIG. 15 illustrates another method for determining an ablation treatmentbased on a tilted orientation according to an embodiment of the presentinvention.

DETAILED DESCRIPTION OF THE INVENTION

Embodiments of the present invention encompass methods and systems forablation treatment during laser eye surgery. Treatment plans for a laserrefractive surgery may benefit by taking into account a slope of thecornea surface, which affects the ablation depth of a laser pulse. Atreatment plan may account for cornea surface slope by multiplying anominal ablation depth by the cosine of the surface slope at each pulselocation. The cosine may be estimated based on an ellipsoid model forthe cornea surface of the patient's eye. Ellipsoid models of a patient'seye typically assume that the main axis of the ellipsoid as well as thelaser beam light incident on the corneal surface are vertical. Theellipsoid model may be calculated from two curvature values and atorsional rotation angle, which may be obtained using a keratometer.

A patient's eyes may be slightly tilted in both an X direction, whichcorresponds to an axis intersecting both eyes, and a Y direction, whichis orthogonal to the X direction. Eye tilt during laser correctionsurgery may correspond to the angle between the visual axis and theoptical axis of the eye. When a patient fixates his or her eye on atarget during a laser treatment procedure, the tilted eye may present anasymmetric surface with respect to the laser beam where the cornealsurface has a steeper slope in one direction than in the oppositedirection with respect to the laser beam. Embodiments of the presentinvention include improved cosine effect techniques, which take intoaccount the surface slope difference or asymmetry, as well as techniquesfor reducing or preventing aberrations that may result from the slopedifference.

Further, the asymmetric surface (e.g., cosine asymmetry) may be alsoaffected by eye shift due to treatment misalignment. Eye shift may occurwhen the corneal vertex is offset from the pupil center. Eye shift asapproximated by an ellipsoid model of the eye with the vertex shiftedwith respect to a laser beam's axis, may cause an asymmetric surfacewith respect to a laser beam where the corneal surface has a steeperslope in one direction than in the opposite as described above.Embodiments of the present invention also include improved cosine effecttechniques which take into account these surface slope differences.

To correct for eye tilt and/or eye shift, a cosine adjustmentcoefficient can be calculated and applied to an ablation treatment plan.The cosine adjustment coefficient may be calculated by constructing amodel that approximates the corneal surface of the patient's eye andthat accounts for eye tilt and/or eye shift. The corneal slopes of themodel can be calculated and adjusted according to the tilted orientationof the corneal surface model to obtain the cosine adjustmentcoefficient. An ideal or target ablation may be modified based on thecosine adjustment coefficient to account for eye tilt and/or eye shift.The ablation energy and/or pulse duration of the laser beam may bevaried based on the modified ablation treatment.

Embodiments of the present invention can be readily adapted for use withexisting laser systems and other optical treatment devices. Althoughsystem, software, and method embodiments of the present invention aredescribed primarily in the context of a laser eye surgery system, itshould be understood that embodiments of the present invention may beadapted for use in alternative eye treatment procedures, systems, ormodalities, such as spectacle lenses, intraocular lenses, accommodatingIOLs, contact lenses, corneal ring implants, collagenous corneal tissuethermal remodeling, corneal inlays, corneal onlays, other cornealimplants or grafts, and the like. Relatedly, systems, software, andmethods according to embodiments of the present invention are wellsuited for customizing any of these treatment modalities to a specificpatient. Thus, for example, embodiments encompass custom intraocularlenses, custom contact lenses, custom corneal implants, and the like,which can be configured to treat or ameliorate any of a variety ofvision conditions in a particular patient based on their unique ocularcharacteristics or anatomy.

Turning now to the drawings, FIG. 1 illustrates a laser eye surgerysystem 10 of the present invention, including a laser 12 that produces alaser beam 14. Laser 12 is optically coupled to laser delivery optics16, which directs laser beam 14 to an eye E of patient P. A deliveryoptics support structure (not shown here for clarity) extends from aframe 18 supporting laser 12. A microscope 20 is mounted on the deliveryoptics support structure, the microscope often being used to image acornea of eye E.

Laser 12 generally comprises an excimer laser, ideally comprising anargon-fluorine laser producing pulses of laser light having a wavelengthof approximately 193 nm. Laser 12 will preferably be designed to providea feedback stabilized fluence at the patient's eye, delivered viadelivery optics 16. The present invention may also be useful withalternative sources of ultraviolet or infrared radiation, particularlythose adapted to controllably ablate the corneal tissue without causingsignificant damage to adjacent and/or underlying tissues of the eye.Such sources include, but are not limited to, solid state lasers andother devices which can generate energy in the ultraviolet wavelengthbetween about 185 and 205 nm and/or those which utilizefrequency-multiplying techniques. Hence, although an excimer laser isthe illustrative source of an ablating beam, other lasers may be used inthe present invention.

Laser system 10 will generally include a computer or programmableprocessor 22. Processor 22 may comprise (or interface with) aconventional PC system including the standard user interface devicessuch as a keyboard, a display monitor, and the like. Processor 22 willtypically include an input device such as a magnetic or optical diskdrive, an internet connection, or the like. Such input devices willoften be used to download a computer executable code from a tangiblestorage media 29 embodying any of the methods of the present invention.Tangible storage media 29 may take the form of a floppy disk, an opticaldisk, a data tape, a volatile or non-volatile memory, RAM, or the like,and the processor 22 will include the memory boards and other standardcomponents of modern computer systems for storing and executing thiscode. Tangible storage media 29 may optionally embody wavefront sensordata, wavefront gradients, a wavefront elevation map, a treatment map, acorneal elevation map, and/or an ablation table. While tangible storagemedia 29 will often be used directly in cooperation with a input deviceof processor 22, the storage media may also be remotely operativelycoupled with processor by means of network connections such as theinternet, and by wireless methods such as infrared, Bluetooth, or thelike.

Laser 12 and delivery optics 16 will generally direct laser beam 14 tothe eye of patient P under the direction of a computer 22. Computer 22will often selectively adjust laser beam 14 to expose portions of thecornea to the pulses of laser energy so as to effect a predeterminedsculpting of the cornea and alter the refractive characteristics of theeye. In many embodiments, both laser beam 14 and the laser deliveryoptical system 16 will be under computer control of processor 22 toeffect the desired laser sculpting process, with the processor effecting(and optionally modifying) the pattern of laser pulses. The pattern ofpulses may by summarized in machine readable data of tangible storagemedia 29 in the form of a treatment table, and the treatment table maybe adjusted according to feedback input into processor 22 from anautomated image analysis system in response to feedback data providedfrom an ablation monitoring system feedback system. Optionally, thefeedback may be manually entered into the processor by a systemoperator. Such feedback might be provided by integrating the wavefrontmeasurement system described below with the laser treatment system 10,and processor 22 may continue and/or terminate a sculpting treatment inresponse to the feedback, and may optionally also modify the plannedsculpting based at least in part on the feedback. Measurement systemsare further described in U.S. Pat. No. 6,315,413, the full disclosure ofwhich is incorporated herein by reference.

Laser beam 14 may be adjusted to produce the desired sculpting using avariety of alternative mechanisms. The laser beam 14 may be selectivelylimited using one or more variable apertures. An exemplary variableaperture system having a variable iris and a variable width slit isdescribed in U.S. Pat. No. 5,713,892, the full disclosure of which isincorporated herein by reference. The laser beam may also be tailored byvarying the size and offset of the laser spot from an axis of the eye,as described in U.S. Pat. Nos. 5,683,379, 6,203,539, and 6,331,177, thefull disclosures of which are incorporated herein by reference.

Still further alternatives are possible, including scanning of the laserbeam over the surface of the eye and controlling the number of pulsesand/or dwell time at each location, as described, for example, by U.S.Pat. No. 4,665,913, the full disclosure of which is incorporated hereinby reference; using masks in the optical path of laser beam 14 whichablate to vary the profile of the beam incident on the cornea, asdescribed in U.S. Pat. No. 5,807,379, the full disclosure of which isincorporated herein by reference; hybrid profile-scanning systems inwhich a variable size beam (typically controlled by a variable widthslit and/or variable diameter iris diaphragm) is scanned across thecornea; or the like. The computer programs and control methodology forthese laser pattern tailoring techniques are well described in thepatent literature.

Additional components and subsystems may be included with laser system10, as should be understood by those of skill in the art. For example,spatial and/or temporal integrators may be included to control thedistribution of energy within the laser beam, as described in U.S. Pat.No. 5,646,791, the full disclosure of which is incorporated herein byreference. Ablation effluent evacuators/filters, aspirators, and otherancillary components of the laser surgery system are known in the art.Further details of suitable systems for performing a laser ablationprocedure can be found in commonly assigned U.S. Pat. Nos. 4,665,913,4,669,466, 4,732,148, 4,770,172, 4,773,414, 5,207,668, 5,108,388,5,219,343, 5,646,791 and 5,163,934, the complete disclosures of whichare incorporated herein by reference. Suitable systems also includecommercially available refractive laser systems such as thosemanufactured and/or sold by Alcon, Bausch & Lomb, Nidek, WaveLight,LaserSight, Schwind, Zeiss-Meditec, and the like. Basis data can befurther characterized for particular lasers or operating conditions, bytaking into account localized environmental variables such astemperature, humidity, airflow, and aspiration.

FIG. 2 is a simplified block diagram of an exemplary computer system 22that may be used by the laser surgical system 10 of the presentinvention. Computer system 22 typically includes at least one processor52 which may communicate with a number of peripheral devices via a bussubsystem 54. These peripheral devices may include a storage subsystem56, comprising a memory subsystem 58 and a file storage subsystem 60,user interface input devices 62, user interface output devices 64, and anetwork interface subsystem 66. Network interface subsystem 66 providesan interface to outside networks 68 and/or other devices, such as thewavefront measurement system 30.

User interface input devices 62 may include a keyboard, pointing devicessuch as a mouse, trackball, touch pad, or graphics tablet, a scanner,foot pedals, a joystick, a touchscreen incorporated into the display,audio input devices such as voice recognition systems, microphones, andother types of input devices. User input devices 62 will often be usedto download a computer executable code from a tangible storage media 29embodying any of the methods of the present invention. In general, useof the term “input device” is intended to include a variety ofconventional and proprietary devices and ways to input information intocomputer system 22.

User interface output devices 64 may include a display subsystem, aprinter, a fax machine, or non-visual displays such as audio outputdevices. The display subsystem may be a cathode ray tube (CRT), aflat-panel device such as a liquid crystal display (LCD), a projectiondevice, or the like. The display subsystem may also provide a non-visualdisplay such as via audio output devices. In general, use of the term“output device” is intended to include a variety of conventional andproprietary devices and ways to output information from computer system22 to a user.

Storage subsystem 56 can store the basic programming and data constructsthat provide the functionality of the various embodiments of the presentinvention. For example, a database and modules implementing thefunctionality of the methods of the present invention, as describedherein, may be stored in storage subsystem 56. These software modulesare generally executed by processor 52. In a distributed environment,the software modules may be stored on a plurality of computer systemsand executed by processors of the plurality of computer systems. Storagesubsystem 56 typically comprises memory subsystem 58 and file storagesubsystem 60.

Memory subsystem 58 typically includes a number of memories including amain random access memory (RAM) 70 for storage of instructions and dataduring program execution and a read only memory (ROM) 72 in which fixedinstructions are stored. File storage subsystem 60 provides persistent(non-volatile) storage for program and data files, and may includetangible storage media 29 (FIG. 1) which may optionally embody wavefrontsensor data, wavefront gradients, a wavefront elevation map, a treatmentmap, and/or an ablation table. File storage subsystem 60 may include ahard disk drive, a floppy disk drive along with associated removablemedia, a Compact Digital Read Only Memory (CD-ROM) drive, an opticaldrive, DVD, CD-R, CD-RW, solid-state removable memory, and/or otherremovable media cartridges or disks. One or more of the drives may belocated at remote locations on other connected computers at other sitescoupled to computer system 22. The modules implementing thefunctionality of the present invention may be stored by file storagesubsystem 60.

Bus subsystem 54 provides a mechanism for letting the various componentsand subsystems of computer system 22 communicate with each other asintended. The various subsystems and components of computer system 22need not be at the same physical location but may be distributed atvarious locations within a distributed network. Although bus subsystem54 is shown schematically as a single bus, alternate embodiments of thebus subsystem may utilize multiple busses.

Computer system 22 itself can be of varying types including a personalcomputer, a portable computer, a workstation, a computer terminal, anetwork computer, a control system in a wavefront measurement system orlaser surgical system, a mainframe, or any other data processing system.Due to the ever-changing nature of computers and networks, thedescription of computer system 22 depicted in FIG. 2 is intended only asa specific example for purposes of illustrating one embodiment of thepresent invention. Many other configurations of computer system 22 arepossible having more or less components than the computer systemdepicted in FIG. 2.

Referring now to FIG. 3, one embodiment of a wavefront measurementsystem 30 is schematically illustrated in simplified form. In verygeneral terms, wavefront measurement system 30 is configured to senselocal slopes of a gradient map exiting the patient's eye. Devices basedon the Hartmann-Shack principle generally include a lenslet array tosample the gradient map uniformly over an aperture, which is typicallythe exit pupil of the eye. Thereafter, the local slopes of the gradientmap are analyzed so as to reconstruct the wavefront surface or map.

More specifically, one wavefront measurement system 30 includes an imagesource 32, such as a laser, which projects a source image throughoptical tissues 34 of eye E so as to form an image 44 upon a surface ofretina R. The image from retina R is transmitted by the optical systemof the eye (e.g., optical tissues 34) and imaged onto a wavefront sensor36 by system optics 37. The wavefront sensor 36 communicates signals toa computer system 22′ for measurement of the optical errors in theoptical tissues 34 and/or determination of an optical tissue ablationtreatment program. Computer 22′ may include the same or similar hardwareas the computer system 22 illustrated in FIGS. 1 and 2. Computer system22′ may be in communication with computer system 22 that directs thelaser surgery system 10, or some or all of the components of computersystem 22, 22′ of the wavefront measurement system 30 and laser surgerysystem 10 may be combined or separate. If desired, data from wavefrontsensor 36 may be transmitted to a laser computer system 22 via tangiblemedia 29, via an I/O port, via an networking connection 66 such as anintranet or the Internet, or the like.

Wavefront sensor 36 generally comprises a lenslet array 38 and an imagesensor 40. As the image from retina R is transmitted through opticaltissues 34 and imaged onto a surface of image sensor 40 and an image ofthe eye pupil P is similarly imaged onto a surface of lenslet array 38,the lenslet array separates the transmitted image into an array ofbeamlets 42, and (in combination with other optical components of thesystem) images the separated beamlets on the surface of sensor 40.Sensor 40 typically comprises a charged couple device or “CCD,” andsenses the characteristics of these individual beamlets, which can beused to determine the characteristics of an associated region of opticaltissues 34. In particular, where image 44 comprises a point or smallspot of light, a location of the transmitted spot as imaged by a beamletcan directly indicate a local gradient of the associated region ofoptical tissue.

Eye E generally defines an anterior orientation ANT and a posteriororientation POS. Image source 32 generally projects an image in aposterior orientation through optical tissues 34 onto retina R asindicated in FIG. 3. Optical tissues 34 again transmit image 44 from theretina anteriorly toward wavefront sensor 36. Image 44 actually formedon retina R may be distorted by any imperfections in the eye's opticalsystem when the image source is originally transmitted by opticaltissues 34. Optionally, image source projection optics 46 may beconfigured or adapted to decrease any distortion of image 44.

In some embodiments, image source optics 46 may decrease lower orderoptical errors by compensating for spherical and/or cylindrical errorsof optical tissues 34. Higher order optical errors of the opticaltissues may also be compensated through the use of an adaptive opticelement, such as a deformable mirror (described below). Use of an imagesource 32 selected to define a point or small spot at image 44 uponretina R may facilitate the analysis of the data provided by wavefrontsensor 36. Distortion of image 44 may be limited by transmitting asource image through a central region 48 of optical tissues 34 which issmaller than a pupil 50, as the central portion of the pupil may be lessprone to optical errors than the peripheral portion. Regardless of theparticular image source structure, it will be generally be beneficial tohave a well-defined and accurately formed image 44 on retina R.

In one embodiment, the wavefront data may be stored in a computerreadable medium 29 or a memory of the wavefront sensor system 30 in twoseparate arrays containing the x and y wavefront gradient valuesobtained from image spot analysis of the Hartmann-Shack sensor images,plus the x and y pupil center offsets from the nominal center of theHartmann-Shack lenslet array, as measured by the pupil camera 51 (FIG.3) image. Such information contains all the available information on thewavefront error of the eye and is sufficient to reconstruct thewavefront or any portion of it. In such embodiments, there is no need toreprocess the Hartmann-Shack image more than once, and the data spacerequired to store the gradient array is not large. For example, toaccommodate an image of a pupil with an 8 mm diameter, an array of a20×20 size (i.e., 400 elements) is often sufficient. As can beappreciated, in other embodiments, the wavefront data may be stored in amemory of the wavefront sensor system in a single array or multiplearrays.

While the methods of the present invention will generally be describedwith reference to sensing of an image 44, a series of wavefront sensordata readings may be taken. For example, a time series of wavefront datareadings may help to provide a more accurate overall determination ofthe ocular tissue aberrations. As the ocular tissues can vary in shapeover a brief period of time, a plurality of temporally separatedwavefront sensor measurements can avoid relying on a single snapshot ofthe optical characteristics as the basis for a refractive correctingprocedure. Still further alternatives are also available, includingtaking wavefront sensor data of the eye with the eye in differingconfigurations, positions, and/or orientations. For example, a patientwill often help maintain alignment of the eye with wavefront measurementsystem 30 by focusing on a fixation target, as described in U.S. Pat.No. 6,004,313, the full disclosure of which is incorporated herein byreference. By varying a position of the fixation target as described inthat reference, optical characteristics of the eye may be determinedwhile the eye accommodates or adapts to image a field of view at avarying distance and/or angles.

The location of the optical axis of the eye may be verified by referenceto the data provided from a pupil camera 52. In the exemplaryembodiment, a pupil camera 52 images pupil 50 so as to determine aposition of the pupil for registration of the wavefront sensor datarelative to the optical tissues.

An alternative embodiment of a wavefront measurement system isillustrated in FIG. 3A. The major components of the system of FIG. 3Aare similar to those of FIG. 3. Additionally, FIG. 3A includes anadaptive optical element 53 in the form of a deformable mirror. Thesource image is reflected from deformable mirror 98 during transmissionto retina

R, and the deformable mirror is also along the optical path used to formthe transmitted image between retina R and imaging sensor 40. Deformablemirror 98 can be controllably deformed by computer system 22 to limitdistortion of the image formed on the retina or of subsequent imagesformed of the images formed on the retina, and may enhance the accuracyof the resultant wavefront data. The structure and use of the system ofFIG. 3A are more fully described in U.S. Pat. No. 6,095,651, the fulldisclosure of which is incorporated herein by reference.

The components of an embodiment of a wavefront measurement system formeasuring the eye and ablations may comprise elements of a WaveScan®system, available from Abbott Medical Optics Inc., Santa Ana, Calif. Oneembodiment includes a WaveScan system with a deformable mirror asdescribed above. An alternate embodiment of a wavefront measuring systemis described in U.S. Pat. No. 6,271,915, the full disclosure of which isincorporated herein by reference. It is appreciated that any wavefrontaberrometer could be employed for use with the present invention.Relatedly, embodiments of the present invention encompass theimplementation of any of a variety of optical instruments provided byAMO WaveFront Sciences, LLC, including the COAS wavefront aberrometer,the ClearWave contact lens aberrometer, the CrystalWave IOL aberrometer,and the like.

Tilt Induced Asymmetry and Aberrations

Referring now to FIG. 4A, illustrated is a two dimensional approximationof an eye's surface in the Z-X plane. The eye's surface is approximatedas an ellipse 400, although the approximation could include othershapes, such as a biconic. The major axis 401 of the ellipse is alignedwith the Z axis so that the corneal vertex 404 of the approximated eye(e.g., the point on the upper portion of the ellipse where the tangentis parallel to the x axis) is equivalent to the apex 402 of the ellipse(e.g., the point where the major axis 401 intersects the upper portionof the ellipse). In such a configuration, the Z axis axially aligns withthe optical axis of the eye. The approximated eye ellipsoid shape may becalculated from two curvature values of a patient's eye and thetorsional rotation angle of the ellipsoid. The curvature values and/ortorsional rotation angle may be obtained by a keratometer.

In laser ablation treatments the laser beam is typically axially alignedwith the Z axis. Due to the sloped contour of the cornea surface,ablations of the cornea experience a cosine effect as the ablations moveradially outward from the Z axis. As shown in FIG. 4B, as the laser beammoves to the peripheral cornea a distance X from the Z axis, the laserbeam incident upon the corneal surface of the eye experiencesovalization due to the curved surface of the cornea. Likewise, as shownin FIG. 4C, a portion of the laser beam is reflected from the peripheralcornea surface due to the lack of perpendicular energy being deliveredto the cornea. The laser beam energy is attenuated at the peripheralcornea due to ovalization and reflection, which affects the ablationdepth per a laser pulse. Steeper corneal slope profiles may result inlarger cosine effects compared to gradual corneal slope profiles. Toaccount for the cosine effect, a laser ablation treatment may employ acosine adjustment measure, which may include multiplying a nominalablation depth by the cosine of the surface slope at each pulselocation. For example, the intensity of the laser beam energy and/or theduration of the laser treatment at the peripheral corneal portions maybe increased to compensate for the cosine effect of the measured cornealsurface profile. An example of such an ablation treatment procedure isprovided in commonly assigned U.S. Pat. No. 7,419,485, the fulldisclosure of which is incorporated herein by reference.

In some instances the patient's eye may be slightly tilted in relationto the axis of the laser beam. FIG. 5A, illustrates an approximation ofa tilted profile for an eye surface in the Z-X plane. As in FIG. 4A, theZ axis typically corresponds to the axis of the laser beam. In thetilted orientation, the approximated corneal vertex of the eye 502 isoffset from the apex 504 and/or the Z axis. The tilted orientationresults in an asymmetric corneal surface relative to the corneal vertex502 where the corneal surface has a different surface slope in onedirection measured from the corneal vertex (plus X direction of FIG. 5A)than in the opposite direction (minus X direction of FIG. 5A). Theresult is generally that the surface slope is steeper in one directionthan in the opposite direction. The tilted orientation produces anasymmetric cosine effect at opposite peripheral corneal edges.Embodiments of the present invention provide treatment systems andmethods which take into account the asymmetry as well as any alignmentvariations between the laser treatment device and the patient's eye. Forexample, the treatment target, which is aligned with the pupil center,may be offset from the corneal vertex of the approximated patient's eye.This may also produce an asymmetric cosine effect at opposite peripheralcorneal edges.

Although FIG. 5A illustrates a tilted orientation of an ellipsoidapproximation of the eye in the Z-X plane, the patient's eye may have asimilar tilted orientation in the Z-Y plane. The tilted orientation of apatient's eye may correspond to the angle between the visual axis 512(i.e., the axis from the center of the pupil to the fovea 510) andoptical axis 506 (i.e., the axis through the center of the cornea andthe apex 504). In the tilted orientation, the optical axis 506 of thepatient's eye is typically angularly offset from the axis of the laserbeam. The tilted orientation of the patient's eye may be apparent as thepatient fixates his or her eye on a target on during a laser ablationtreatment.

FIGS. 5D-E provide a histogram of measured eye tilts in degrees forpatients' left and right eyes in an x direction (i.e., a directiongenerally parallel to an axis intersecting both eyes) and a y directionorthogonal to the x direction. The eye tilts are measured from the Zaxis, which corresponds to an axis extending from a target the patientfixates on to the center of the ellipsoid approximation. FIGS. 5D-Eillustrate that the right eye (OD) is generally negatively rotated fromthe Z axis while the left eye (OS) is generally positively rotated fromthe Z axis. The result is that the visual axis of both eyes is typicallyon the nasal side of the optical axis. FIGS. 5D-E also illustrate thatthe tilt for both right and left eyes are negative in the y direction,resulting in both eyes typically pointing slightly vertically downward.

The mean tilt and standard deviation for the left and right eyes in thex direction is provided in table 1 below. As illustrated, the meanvalues for horizontal tilts (x direction) are approximately half thetypical value reported for the angle (i.e., 5 deg) between the eye'svisual axis and optical axis.

TABLE 1 Horizontal eye tilt statistics for left and right eyes OD OS Txmean std mean std deg −1.7 2.7 2.3 2.9

Using the formulas provided below, the cosine effect asymmetry of theeye's tilted orientation may be calculated.

a. Equations for an Ellipsoid with No Tilt

The equation for an ellipsoid with no tilt is:

$\begin{matrix}{{\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} + \frac{z^{2}}{c^{2}}} = 1} & \left( {A\; 1} \right)\end{matrix}$

To find the surface slope of an non-tilted ellipsoid at any point (x, y)on the ellipsoid surface, the following equations may be used:

A general quadric surface can be described by:

$\begin{matrix}{{{{P(1)} \cdot x^{2}} + {{P(2)} \cdot y^{2}} + {{P(3)} \cdot z^{2}} + {{P(4)} \cdot {xy}} + {{P(5)} \cdot {xz}} + {{P(6)} \cdot {yz}} + {{P(7)} \cdot x} + {{P(8)} \cdot y} + {{P(9)} \cdot z}} = 1} & ({B1})\end{matrix}$

For a given point on the surface with coordinates x,y, the height of thesurface at this point is:

$\begin{matrix}{z = \frac{{- B} + \sqrt{B^{2} - {4 \cdot {P(3)} \cdot C}}}{2{P(3)}}} & \left( {B\; 2} \right)\end{matrix}$

B and C are defined by the following equations:

B=P(5)·x+P(6)·y+P(9)

C=P(1)·x ² +P(2)·y ² +P(4)·xy+P(7)·x+P(8)·y−1  (B3)

From (B1) we can find the differential form:

$\begin{matrix}{{{{P(1)} \cdot x \cdot {dx}} + {{P(2)} \cdot y \cdot {dy}} + {{P(3)} \cdot z \cdot {dz}} + {{P(4)} \cdot x \cdot {dy}} + {{P(4)} \cdot {dx} \cdot y} + {{P(5)} \cdot x \cdot {dz}} + {{P(5)} \cdot {dx} \cdot z} + {{P(6)} \cdot y \cdot {dz}} + {{P(6)} \cdot {dy} \cdot z} + {{P(7)} \cdot {dx}} + {{P(8)} \cdot {dy}} + {{P(9)} \cdot {dz}}} = 1} & ({B4})\end{matrix}$

This gives us the surface gradient components:

$\begin{matrix}{{\frac{\partial z}{\partial x} = {- \frac{{P{(1) \cdot x}} + {{P(4)} \cdot y} + {{P(5)} \cdot z} + {P(7)}}{{{P(3)} \cdot z} + {{P(5)} \cdot x} + {{P(6)} \cdot y} + {P(9)}}}}{\frac{\partial z}{\partial y} = {- \frac{{P{(2) \cdot y}} + {{P(4)} \cdot x} + {{P(6)} \cdot z} + {P(8)}}{{{P(3)} \cdot z} + {{P(5)} \cdot x} + {{P(6)} \cdot y} + {P(9)}}}}} & ({B5})\end{matrix}$

The slope of the non-tilted surface (∇z) is:

$\begin{matrix}\begin{matrix}{{{\nabla z}} = \sqrt{\left( \frac{\partial z}{\partial x} \right)^{2} + \left( \frac{\partial z}{\partial y} \right)^{2}}} \\{= \sqrt{\frac{\begin{matrix}{\left( {{{P(1)} \cdot x} + {{P(4)} \cdot y} + {{P(5)} \cdot z} + {P(7)}} \right)^{2} +} \\\left( {{{P(2)} \cdot y} + {{P(4)} \cdot x} + {{P(6)} \cdot z} + {P(6)}} \right)^{2}\end{matrix}}{\left( {{{P(3)} \cdot z} + {{P(5)} \cdot x} + {{P(6)} \cdot y} + {P(9)}} \right)}}}\end{matrix} & ({B6})\end{matrix}$

b. Equations for an Ellipsoid Tilted in the X Direction

Referring to FIG. 5A, the following notations are used in the equationsbelow:

φ—angle of a radius to a point on the ellipse, relative to the verticalaxis Z;

φ_(T)—angle of the ellipse tilt, i.e. angle of the ellipse apex relativeto the vertical axis;

φ_(F)—angle of the ellipse vertex, where the ellipse surface ishorizontal;

φ_(R)—angle of the ellipse point, located at the distance +X from thevertex;

φ_(L)—angle of the ellipse point, located at the distance −X from thevertex;

α—angle of the ellipse surface slope;

α_(R)—angle of the ellipse surface slope at the distance +X from thevertex;

α_(R)—angle of the ellipse surface slope at the distance −X from thevertex.

For a non-tilted ellipse the angle φ of the point at the distance X fromthe ellipse apex 402 (see FIG. 4A—for a non-tilted ellipse, the apex isthe same as the vertex) is:

$\begin{matrix}{{\tan \; \varphi} = \frac{X/c}{\sqrt{1 - \left( {X/a} \right)^{2}}}} & ({A2})\end{matrix}$

The slope of a non-tilted ellipse at the distance X from the apex is:

$\begin{matrix}{{\tan \; \alpha} = {{\left( \frac{c}{a} \right)^{2}\frac{X/c}{\sqrt{1 - \left( {x/a} \right)^{2}}}} = {\left( \frac{c}{a} \right)^{2}\tan \; \varphi}}} & ({A3})\end{matrix}$

From the equation for an ellipse (A1 above) with y=0, the radius (r)from the center of the ellipse at the angle φ is:

$\begin{matrix}{r = \left( {\frac{\cos^{2}\varphi}{c^{2}} + \frac{\sin^{2}\varphi}{a^{2\;}}} \right)^{{- 1}/2}} & ({A4})\end{matrix}$

From the equation A3, the slope as a function of the angle φ relative tothe vertical axis can be determined:

$\begin{matrix}{{\tan \left( {\alpha - \varphi_{T}} \right)} = {\left( \frac{c}{a} \right)^{2}{\tan \left( {\varphi - \varphi_{T}} \right)}}} & ({A5})\end{matrix}$

Since the vertex is defined as a point with zero slope in the tiltedorientation (i.e., the topmost point on the ellipse), the angle φ_(V) ofthe vertex may be determined by the following equation:

$\begin{matrix}{{\tan \left( {- \varphi_{T}} \right)} = {\left( \frac{c}{a} \right)^{2}{\tan \left( {\varphi_{V} - \varphi_{T}} \right)}}} & ({A6})\end{matrix}$

This provides the following equation for φ_(F):

$\begin{matrix}{\varphi_{V} = {\varphi_{T} - {{atan}\left( {\left( \frac{a}{c} \right)^{2}\tan \; \varphi_{T}} \right)}}} & ({A7})\end{matrix}$

Using equation A4, the ellipse radius at the angle φ can be derived fromthe following equation:

$\begin{matrix}{{r(\varphi)} = \left( {\frac{\cos^{2}\left( {\varphi - \varphi_{T}} \right)}{c^{2}} + \frac{\sin^{2}\left( {\varphi - \varphi_{T}} \right)}{a^{2}}} \right)^{{- 1}/2}} & ({A8})\end{matrix}$

The angle φ of a point at the distance X from the ellipse vertex can bedetermined using the function in A8 by solving the following equation:

X=r(φ)·sin(φ)−r(φ_(v))·sin(φ_(V))  (A9)

Once the angle φ(X) for a point is determined, the surface slope at thispoint can be calculated using the formula in A5:

$\begin{matrix}{\alpha = {{{atan}\left\lbrack {\left( \frac{c}{a} \right)^{2}{\tan \left( {{\varphi (X)} - \varphi_{T}} \right)}} \right\rbrack} + \varphi_{T}}} & ({A10})\end{matrix}$

c. Equations for an Ellipsoid Tilted in the X and Y Directions

The surface slope of the entire 2D surface of the ellipsoid tilted inboth the X and Y directions can be determined by transforming equationA1 for a tilted ellipsoid as follows:

$\begin{matrix}{{\frac{\left( {{x\; {\cos \left( \varphi_{T} \right)}} - {z\; {\sin \left( \varphi_{T} \right)}}} \right)^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} + \frac{\left( {{x\; {\sin \left( \varphi_{T} \right)}} + {z\; {\cos \left( \varphi_{T} \right)}}} \right)^{2}}{c^{2}}} = 1} & ({A11})\end{matrix}$

From this equation the differential form is determined as:

$\begin{matrix}{{{\frac{\left( {{x\; {\cos \left( \varphi_{T} \right)}} - {z\; {\sin \left( \varphi_{T} \right)}}} \right)}{a^{2}}{dx}} + {\frac{y}{b^{2}}{dy}} + {\frac{\left( {{x\; {\sin \left( \varphi_{T} \right)}} + {z\; {\cos \left( \varphi_{T} \right)}}} \right)}{c^{2}}{dz}}} = 0} & ({A12})\end{matrix}$

This provides an equation for the surface slope (∇z(φ_(T))) of thetilted ellipsoid:

$\begin{matrix}{{{\nabla{z\left( \varphi_{T} \right)}}} = {\sqrt{\left( \frac{\partial z}{\partial x} \right)^{2} + \left( \frac{\partial z}{\partial y} \right)^{2}} = \sqrt{\begin{matrix}{\left( \frac{{x^{\prime}{{\cos \left( \varphi_{T} \right)}/a^{2}}} + {z^{\prime}{{\sin \left( \varphi_{T} \right)}/c^{2}}}}{{x^{\prime}{{\sin \left( \varphi_{T} \right)}/a^{2}}} - {z^{\prime}{{\cos \left( \varphi_{T} \right)}/c^{2}}}} \right)^{2} +} \\\left( \frac{y/b^{2}}{{x^{\prime}{{\sin \left( \varphi_{T} \right)}/a^{2}}} - {z^{\prime}{{\cos \left( \varphi_{T} \right)}/c^{2}}}} \right)^{2}\end{matrix}}}} & ({A13})\end{matrix}$

FIGS. 5B-C provide graphical illustrations of the cosine effectasymmetry in the X-Z plane due to the tilted orientation of a patient'seye. Specifically, FIG. 5B illustrates the cosine of the surface slopeof a patient's eye in the x direction for an un-tilted eye, a mean eyetilt of 5 degrees, and a maximum eye tilt of 11 degrees of an eyeapproximated having a major axis of 11.7 mm (i.e., c=11.7 mm) and aminor axis of 9.4 mm (i.e., a=9.4 mm). The surface slope cosines werecalculated to a distance of approximately 5 mm on both sides of thecorneal vertex (see FIG. 5A).

As illustrated in FIG. 5B, an un-tilted eye has a symmetrical surfaceslope cosine profile with a cosine of approximately 0.78 at 5 mm oneither side of the corneal vertex. With a tilt of 5 degrees, the cosineasymmetry is such that the cosine value at −5 mm from the corneal vertexis approximately 0.80 and the cosine value at +5 mm from the cornealvertex is approximately 0.76. A tilt of 11 degrees produces a moredrastic asymmetry with a cosine value of approximately 0.83 at −5 mm anda cosine value of approximately 0.73 at +5 mm. Similarly, FIG. 5Cillustrates the ratio of the cosine value of a mean tilt of 5 degreesand the cosine value of a max tilt of 11 degrees versus the cosine valueof an un-tilted eye. FIG. 5C illustrates that the cosine valuesincreasingly deviate from symmetry (about the corneal vertex) as thetilt orientation increases. While FIGS. 5A-C focus on a tilted cornealsurface in the X-Z plane, these figures and the accompanying descriptionare merely illustrative of the cosine asymmetry due to the tiltedorientation and it should be realized that such asymmetry may occur inany plane of the ellipsoid. As described in the equations above, thesurface slope of the entire 2D surface of the tilted ellipsoid can bedetermined so that the cosine asymmetry of the patient's entire cornealsurface is known.

The cosine asymmetry due to the tilted orientation may result in theformation of ablation treatment induced aberrations. For example, thecosine asymmetry may deviate the actual ablation of corneal tissue fromthe target or ideal ablation treatment, which may cause high-orderaberrations to appear, such as spherical aberrations or Coma. Given theablation refraction and the characteristics of the corneal profile ofthe eye, the high order aberrations that may be induced from the cosineasymmetry may be estimated as provided below in the examples section.

Using the surface slope values of the ellipsoid surface (eithernon-tilted, tilted, or both), the cosine values may be calculated and acosine adjustment measure determined for one or more points (x, y) onthe ellipsoid surface. Using the cosine adjustment measure, an ablationtreatment may be modified or adjusted to account for the tilt of thepatient's eye. This may reduce or substantially eliminate the formationof ablation treatment induced aberrations. For example, using thesurface slopes of the ellipsoid surface (both the non-tilted surfaceslopes and the tilted surface slopes above), a adjustment coefficient,C_(asym), may be obtained for the entire corneal surface of the eye fromthe following equation:

C _(asym) =|∇z(φ_(T))|/|∇z(0)|

The equations for ∇z(φ_(T)) and ∇z(0) are provided and described above.See e.g., equations (A13) and (B6) respectively. Using the adjustmentcoefficient, C_(asym), a target or ideal ablation treatment A₀ may bemodified or adjusted to account for tilt by multiplying the idealablation treatment by the adjustment coefficient: A₀*C_(asym). In thismanner an ablation treatment may account for the cosine asymmetry of theeye due to tilt and thereby reduce or eliminate the formation ofablation induced aberrations.

In some embodiments it may be desirous to include or retain a certainamount of induced high order aberrations, such as to increase depth offocus. In such embodiments the amount of induced high order aberrationsmay be controlled rather than eliminated. As such, the equationsdescribed herein may be used and/or modified to control induced highorder aberrations rather than eliminate such aberrations.

As mentioned above, cosine asymmetry may also be caused or furtherenhanced by de-centering of the treatment device. De-centering may occurwhen the laser beam is not aligned with the corneal vertex of the tiltedeye. Asymmetry due to de-centering may result in the formation ofablation induced high-order aberrations, such as spherical aberrations,Coma, and the like. FIG. 6A illustrates estimated coma inducement due tode-centering for various diopters and various de-centering shifts. Theestimates were calculated from an ellipsoid model with the followingparameters: a=9.2 mm, b=9.2 mm, and c=11.2 mm. With a magnitude ofde-centering, 0.3 mm, the shift-induced coma may reach 0.1 um forhigh-myopia treatments (e.g., 8-10 D).

FIG. 6B illustrates a cosine asymmetry adjustment coefficient for an 8diopter myopia eye having a 0.3 mm de-centering shift in the Xdirection. The equations presented above may be modified to account forde-centering of the laser ablation treatment. The modifications can bedone by shifting X and Y coordinates as follows:

X′=X+ΔXpupil

Y′=Y+ΔYpupil

Here X′ and Y′ are the new coordinates, which should be used in place ofX and Y in the formulas above. ΔXpupil and ΔYpupil are the shifts of thepupil center relative to the vertex.

Ablation Treatments based on Tilted Orientation

Referring to FIG. 7, illustrated is a flow diagram 700 of a method fordetermining an ablation treatment based on a tilted orientation of apatient's eye. In some cases, the determination may involve modifying oradjusting an ablation treatment to account for cosine asymmetry due tothe tilted orientation. At block 704, an ellipsoid shape may bedetermined that approximates the corneal surface of the patient's eye.The parameters for the ellipsoid shape may be determined through avariety of factors. For example, a keratometry measurement may beperformed to obtain the curvature value of the steepest meridian of thepatient's eye (k1 value), the curvature value of the meridian orthogonalto the steepest meridian (k2 value), and the torsional rotation angle(k2A value). These three parameters may be used to construct a cornealellipsoid that approximates the patient's eye. Alternatively oradditionally, a corneal topography elevation map H(x, y) may be measuredand/or obtained for the corneal surface of the patient's eye, from whichan ellipsoid model may be constructed.

According to another embodiment, population averages may be obtained forcorneal ellipsoid shapes and a corneal ellipsoid may be constructed fromthe population average values to approximate the corneal surface of thepatient's eye. Further, another model shape may be constructed toapproximate the patient's eye, such as a biconic or other shape. Thebiconic shape and/or other model shape may be based on topographymeasurements, keratometry measurements, and/or population averagemeasurements.

At block 708, the tilted orientation of the ellipsoid shape (or othershape) may be determined. For example, according to one embodiment, acorneal topography elevation map H(x, y) may be fitted onto the modelellipsoid shape to determine the tilted orientation. A Linearleast-square fit, or any other optimization technique, can be used toadjust the ellipsoid model parameters until the model shape best fitsthe topography data. Examples of least-square fit techniques aregenerally described in “Solving Least Square Problems,” L. L. Lawson, R.J. Hanson, Prentice-Hall, Inc., Englewood Cliffs, N.J. , 1974, which isincorporated by reference herein. Fitting the topography data onto themodel ellipsoid or other shape yields the model shape parameters. For anellipsoid, these model shape parameters include the axes sizes (i.e., a,b, & c of equation A1), the apex position, and the like. Alternativelyor additionally, population averages may be obtained for the tiltedorientation of patients' eyes and a tilted corneal ellipsoid may beconstructed from the population average values to approximate the tiltedorientation of the corneal surface of the patient's eye.

The measured and/or calculated model ellipsoid parameters for thepatient's eye may be compared against the population averages and awarning may be produced if the patient's model ellipsoid parametersappear beyond a pre-defined population average criteria (e.g., beyond 3times the standard deviation). Similarly, an offset of the cornealvertex relative to the pupil center may be obtained and/or determined.This offset value may be used with the model parameters to determine amodel surface (i.e., ellipsoid) that approximates the patient's eye.

At block 712, an ablation treatment for the patient may be determinedbased on the ellipsoid shape and the tilted orientation. For example,the corneal surface slopes (i.e., non-tilted, tilted, or both) in theablation area may be calculated and a cosine adjustment coefficient,C_(asym), may be determined and applied to an ideal or target ablationA₀. From the model shape parameters, the equations above may be used todetermine the surface slopes of the ellipsoid and the adjustmentcoefficient, C_(asym), may be determined.

In some embodiments, treatment plans or shapes based on the measuredtopography and/or keratometry data may be adjusted or further definedbased on measured patient wavefront data. For example, after the cosineadjustment coefficient, C_(asym), is applied to the ideal or targetablation A₀, wavefront data may be used to further adjust the ablationtreatment plan. In other embodiments, wavefront data may be used incombination with application of the cosine adjustment coefficient,C_(asym), to the ideal or target ablation A₀ to determine or optimizethe adjusted ablation treatment plan.

Referring now to FIG. 8, illustrated is another flow diagram 800 of amethod for determining an ablation treatment based on a tiltedorientation according to another embodiment of the invention. At block804, a corneal topography elevation map H(x,y) may be obtained fromtopography measurements of the patient's eye and/or from any othersource of data (i.e., manually input by a physician). At block 816, themeasured elevation may be fit onto a model shape (i.e., ellipsoid,biconic, or the like) to determine the model parameters that approximateor best approximate the patient's eye. Alternatively or additionally, atblock 808, keratometry measurements (k1, k2, k2A as described elsewhereherein). The keratometry measurements may be used to determine the modelshape parameters that approximate or best approximate the patient's eye.If topography or keratometry measurements are not available or inaddition to using one or both of these measurements, the populationaverage values for model corneal shapes may be obtained, such as througha database, memory, or other storage device as described herein.

At block 820, the model shape parameters (e.g., corneal ellipsoidparameters) may be determined from the topography elevationmap/measurements, keratometry measurements, and/or population averagesof blocks 804, 808, and 812 respectively. At block 824, a corneal shapemodel (i.e., ellipsoid, biconic, or the like) may be constructed fromthe corneal model parameters. The corneal shape model may approximatethe tilted orientation of the patient's eye. Determining the tiltedorientation may involve fitting the corneal topography elevation maponto the model shape and/or using population average values. At block828, the corneal model parameters may be compared against populationaverages and a warning produced (block 832) if the model parameters falloutside a defined threshold. Although illustrated as occurring afterblock 828, block 832 determination may occur before the corneal model isconstructed. If the model parameters do not fall outside the definedthreshold, the cosine adjustment coefficient can be determined at block836.

FIG. 9, illustrates a method for determining an ablation treatment basedon the tilted orientation of the patient's eye. At block 904, thecorneal slopes are determined based on the corneal surface model (e.g.,corneal ellipsoid). Determining the corneal slopes may involvedetermining both the corneal slopes for the non-tilted corneal surfacemodel and the corneal slopes for the tilted corneal surface model. Atblock 908, an ablation treatment plan is determined based on the cornealsurface slopes to account for the cosine effect of the non-tiltedcorneal surface model. At block 912, the ablation treatment plan isadjusted according to the tilted orientation of the corneal surfacemodel to account for the cosine asymmetry due to the tilt of the cornealsurface model. Determining and/or adjusting the ablation plan in block908 and 912 may involve calculation one or more cosine adjustmentcoefficients to account for the cosine values associated with thesurface slopes and/or the cosine asymmetry due to the tiltedorientation.

Alternatively, adjusting an ablation treatment may involve a single stepor process as shown in block 916 and 920. At block 916, a cosineadjustment coefficient, C_(asym), may be determined based on the surfaceslopes of the non-tilted and tilted corneal model ellipsoid or othershape as described herein. At block 920, an ideal or target ablationtreatment may be adjusted or modified based on the cosine adjustmentcoefficient, C_(asym). Adjusting or modifying the ablation treatment mayinclude multiplying an ideal or target ablation treatment A₀ by thecosine adjustment coefficient, C_(asym) (i.e., A₀*C_(asym)) and/or mayinclude varying the ablation energy and/or pulse duration of theablation laser beam. The ideal or target ablation treatment A₀ may be awavefront guided or determined treatment plan.

Referring now to FIG. 10, illustrated is a flow diagram 1000 of a methodfor determining an ablation treatment based on a tilted orientation thatinvolves using both keratometry and topography measurements. At block1004, keratometry measurements (k1, k2, k2A values) are obtained for thepatient's eye. At block 1008, a corneal model ellipsoid (or other shape)is constructed based on the keratometry measurements. Following arrow“B,” at block 1012, the corneal slopes of the corneal model ellipsoidare optionally calculated based on the corneal model ellipsoid, such asby using the equation (B6) described herein. The corneal slopes may becalculated for the ablation area and/or for any other defined surface ofthe corneal model ellipsoid.

At block 1016, an ablation treatment plan is optionally determinedand/or adjusted based on the corneal slopes calculated in block 1012.Alternatively, the process may not involve the process of blocks 1012and 1016 as shown by the arrow “A” from block 1008 to 1020. At block1020, a corneal topography elevation map may be measured and/orobtained. At block 1024, the corneal measured elevations of thetopography elevation map may be fit onto the corneal ellipsoid modelusing a least square fit or other optimization technique. At block 1028,the tilted orientation of the ellipsoid model may be determined, such asfrom the ellipsoid model parameters determined from fitting the measuredtopography elevations on the model ellipsoid. The tilted orientation maycorrespond to the orientation or position of the patient's eye as thepatient fixates on a target during an ablation treatment. An offset ofthe corneal vertex relative to the pupil center may be obtained and usedto construct the ellipsoid model (either tilted, non-tilted, or both).Further, the corneal slopes within an ablation area or other definedarea may be calculated based on the tilted corneal ellipsoid model toaccount for cosine or other asymmetry.

At block 1032, the model ellipsoid parameters may be compared againstthe population average to determine whether the parameters exceed adefined threshold. If the parameters exceed the defined threshold, awarning may be produced at block 1036 to alert a physician or operatorabout the parameters. If the parameters do not exceed the definedthreshold, an ablation treatment may be modified or adjusted based onthe tilted orientation of the corneal model ellipsoid. Adjusting theablation treatment may include adjusting the treatment determined oradjusting in block 1016 or may include adjusting an ideal or targettreatment A₀ that is a wavefront guided or calculated ablationtreatment. Adjusting the ablation treatment may also include calculatinga cosine adjustment coefficient, C_(asym) based on the corneal slope ofthe tilted and/or non-tilted corneal ellipsoid model.

Referring now to FIG. 11, illustrated is a flow diagram 1100 of a methodfor determining an ablation treatment based on a tilted orientationusing topography measurements. At block 1104, corneal topographyelevations are obtained, such as by accessing a database comprisingtopography measurements, manually inputting the elevation, conducting atopography measurement, etc. At block 1108, a model shape is obtained,such as an ellipsoid shape, biconic shape, etc. The model shape may beconstructed of population averages and/or may be constructed from thetopography elevations obtained at block 1104. At block 112, the measuredand/or obtained topography elevations are fit onto the model shape, suchas by using an optimization technique (e.g., linear least-square).Fitting the topography elevations on the model shape yields theparameters of the model shape (e.g., axes sizes; elements a, b, c ofequation A1, apex position of an ellipsoid, or the like).

At block 1116, the model shape parameters are compared against thepopulation averages to determine if the parameters exceed a definedthreshold. If the parameters exceed the defined threshold, a warning maybe produced at block 1120 to warn a physician or operator. If theparameters do not exceed the defined threshold, at block 1124 an offsetvalue may be obtained that corresponds to an offset of the cornealvertex relative to the pupil center. If this offset value is notavailable, the offset may be assumed to equal 0. At block 1128, ananalytical corneal model may be constructed that approximates thecorneal surface of the patient's eye. The analytical corneal model(e.g., the corneal ellipsoid model) may comprise a tilted orientationcorresponding to the orientation of the patient's eye as the patientfixates on a target during an ablation treatment.

At block 1132, the corneal slopes of the model shape (either non-tilted,tilted, or both) may be calculated. Likewise, a cosine adjustmentcoefficient, C_(asym), may be calculated for the corneal model shape. Atblock 1136, an ablation treatment may be adjusted or modified to accountfor the cosine asymmetry of the tilted corneal model shape. Modifyingthe ablation treatment may include multiplying an ideal or targetablation treatment A₀ by the cosine adjustment coefficient, C_(asym)and/or may include varying the ablation energy and/or pulse duration ofthe laser beam.

Referring now to FIG. 13, illustrated is another flow diagram 1300 of amethod for determining an ablation treatment based on a tiltedorientation according to another embodiment of the invention. At block1302, a corneal topography elevation map H(x,y) may be obtained fromtopography measurements of the patient's eye and/or from any othersource of data (i.e., manually input by a physician). At block 1304, themeasured elevation may be fit onto a model shape (i.e., ellipsoid,biconic, or the like) to determine the model parameters that approximateor best approximate the patient's eye. A linear least square fittechnique may be used (or another optimization technique) to adjust themodel parameters until the model shape fits the topography data. Thismay yield the model parameters. For example, if an ellipsoidapproximation is used this may yield the parameters for the axes sizes,such as parameters a, b, c, and apex position). Alternatively oradditionally, at block 1306, keratometry measurements (k1, k2, k2A asdescribed elsewhere herein) may be obtained for the patient's eye and/orinput by a physician, where the parameter k1 may represent the curvatureof the steepest meridian, k2 may represent the curvature of the meridianorthogonal to the steepest meridian, and k2A may represent the torsionalrotation angle. These three parameters may be used to construct a modelshape (e.g., ellipsoid shape) for the corneal ellipsoid. In someembodiments, the keratometry measurements are used in the absence oftopography measurements, while in other embodiments the keratometrymeasurements are used with or in addition to the topographymeasurements. Using both measurements may provide for a check orconfirmation on the accuracy of the ellipsoid approximation.

At block 1308, the population average of the eye tilts (right and lefteyes) may be combined with the measured keratometry parameters to obtainan approximation of the surface of the tilted corneal ellipsoid. Thismay be used as an alternative or in addition to the topographymeasurements. At block 1314, the measured model parameters may becompared against the population averages. If the measured parametersappear beyond the general population statistics by a defined amount(e.g., greater than three standard deviations or some other amount), awarning may be produced. As an alternative to the process illustrated inblocks 1302 to 1308 or in addition to those processes, at block 1310 thepopulation average for a corneal ellipsoid may be obtained (e.g.,average curvatures, eyes tilts, and the like). The population averagesmay be used to obtain the corneal model parameters (e.g., ellipsoidparameters) and a model approximation of the tilted eye may beconstructed from the model parameters and eye tilts.

At block 1316, the offset of the corneal vertex relative to the pupilcenter may be obtained. If this data is not available, the offset may beassumed to be zero. At block 1318, the model parameters (e.g., ellipsoidparameters, biconic parameters, and the like) and/or the offset valuemay be used to construct an analytical model of the surface of thetilted eye. At block 1320, the analytical model surface may be used tocalculate the corneal slopes in the ablation area as described herein.At block 1322, an adjustment of an ablation treatment for an eye may bedetermined based on the estimated corneal slopes. For example, higher orgreater corneal slopes may require elevated ablation levels. Thedescribed processes steps of FIG. 13 may vary. For example, FIG. 13illustrates that block 1306 may be followed by blocks 1304 and/or 1312so that keratometry and topography measurements are both obtained andfitted onto a model shape used a least squared or other optimizationtechnique. Likewise, topography and/or keratometry measurements may beused with population averages to obtain model parameters and/orconstruct a model shape. In some embodiments, keratometry techniques,topography techniques, and population averages may all be used to obtainmodel parameters and/or construct a model shape. Using multipletechniques may be used to verify the model parameters and/or modelshape.

Referring now to FIG. 14, illustrated is another flow diagram of amethod for determining an ablation treatment based on a tiltedorientation of a patient's eye. At block 1430, a corneal topographyelevation map H(x,y) may be obtained from topography measurements of thepatient's eye and/or from any other source of data (i.e., manually inputby a physician). A corneal surface of a model shape approximating thepatient's eye may be defined by fitting the topography elevations on ananalytical model shape. A linear least-square fit technique may be used(or any other optimization technique) to adjust model parameters untilthe model shape fits the topography data. Similarly, any analyticalmodel, which allows evaluation of the surface tilt, may be used toapproximate the corneal surface. For example, the simples model may bean ellipsoid. Alternative models may include a biconic surface, acemoposition into a series of polynomial functions, and the like.

Alternatively, at block 1420, keratometry measurements (k1, k2, k2A asdescribed elsewhere herein) may be obtained for the patient's eye and/orinput by a physician, where the parameter k1 may represent the curvatureof the steepest meridian, k2 may represent the curvature of the meridianorthogonal to the steepest meridian, and k2A may represent the torsionalrotation angle. The corneal ellipsoid may be defined based on thesemeasurements. The tilt for the corneal ellipsoid may be determined frompopulation tilt averages.

As an alternative to block 1420 and 1430, at block 1410, the cornealellipsoid may be defined based on population averages for ellipsoidparameters. The tilt for the corneal ellipsoid may be determined frompopulation tilt averages.

At block 1440, the measured model parameters may be compared against thepopulation averages. If the measured parameters appear beyond thegeneral population statistics by a defined amount (e.g., greater thanthree standard deviations or some other amount), a warning may beproduced. When population averages are used to define the cornealellipsoid and tilt, the model parameters do not need to be compared topopulation averages at block 1440.

Optionally, at block 1450, the offset of the corneal vertex relative tothe pupil center may be obtained. If this data is not available, theoffset may be assumed to be zero. At block 1460, the model parameters(e.g., ellipsoid parameters, biconic parameters, and the like) and/orthe offset value may be used to construct an analytical model of thesurface of the tilted eye. At block 1470, the analytical model surfacemay be used to calculate the corneal slopes in the entire ablation areaas described herein. At block 1480, an adjustment of an ablationtreatment for an eye may be determined based on the estimated cornealslopes. For example, higher or greater corneal slopes may requireelevated ablation levels.

Referring to FIG. 15, illustrated is a flow diagram 1500 of a method fordetermining an ablation treatment based on a tilted orientation of apatient's eye. In this method, the ablation treatment is determineddirectly from the measurements of a patient's eye. In other words, theablation treatment is determined without having to adjust a pre-existingablation treatment or target ablation A₀. At block 1510, measurements ofa patient's eye are obtained. Obtaining measurements of the patient'seye may involve obtaining topography and/or keratometry measurements asdescribed herein. At block 1520, a tilted orientation of the patient'seye is determined. Determining the tilted orientation of the patient'seye may involve constructing an ellipsoid model shape (or other modelshape) from the measurements of the patient's eye as described herein.At block 1530, an ablation treatment for the patient may be determinedbased on the tilted orientation. The ablation treatment may bedetermined directly from the measurements of the patient's eye and/ordirectly from the tilted orientation without adjusting an ideal ortarget ablation A₀.

EXAMPLES

Using the procedures and formulas described herein a adjustmentcoefficient, C_(asym), was calculated for an eye approximated by anellipse having the following characteristics: a major axis of 11.2 mm(c=11.2 mm), a minor axis of 9.2 mm (a=9.2 mm), a tilted orientation of5 degrees in the x direction, and no tilt in the y direction. The cosineasymmetry adjustment coefficient for the surface of the eye are shown inFIG. 12A. The resulting ablation errors that would result due to thetilt for a myopic ablation profile having no high-order aberrations canbe calculated from the following formula:

${errA} = {\left( {\frac{C_{asym}}{C_{0}} - 1} \right) \cdot A_{myo}}$

The term A_(myo) indicates an ablation treatment profile for a myopiceye and the term C₀ indicates a cosine adjustment measure for anun-tilted ellipsoid (i.e., a cosine adjustment that would be applied toan un-tilted ellipsoid having the above characteristics). The estimatedspherical aberrations and Coma that would result due to the ablationerror are shown in FIG. 12B for different diopters of refractivecorrection of myopia patients. FIG. 12B shows that aberration effectsdue to eye tilt increases with increasing diopter values.

Using the ellipsoid with the above characteristics, the cosine valuescan be calculated for an un-tilted eye and compared with the values fora tilted left and right eye. The cosine values at the edge of an opticalzone having a radius of 3 mm from the corneal vertex and an ablationzone having a radius of 4 mm from the corneal vertex are provided inFIG. 12C. As shown in FIG. 12C, when comparing the maximum values of thestandard deviation bars, the tilt may change the slope cosine value byas much as 0.06.

The cosine value ratio of the tilted eyes (both left and right) tonon-tilted eyes is shown in FIG. 12D. As shown in FIG. 12D, the tiltedorientation of the eyes can vary the cosine value by 1-10%, which asdescribed above may result in ablation treatment induced aberrations(spherical aberrations and/or coma) if not accounted for.

The methods and apparatuses of the present invention may be provided inone or more kits for such use. The kits may comprise a system forprofiling an optical surface, such as an optical surface of an eye, andinstructions for use. Optionally, such kits may further include any ofthe other system components described in relation to the presentinvention and any other materials or items relevant to the presentinvention. The instructions for use can set forth any of the methods asdescribed herein.

Each of the calculations or operations described herein may be performedusing a computer or other processor having hardware, software, and/orfirmware. The various method steps may be performed by modules, and themodules may comprise any of a wide variety of digital and/or analog dataprocessing hardware and/or software arranged to perform the method stepsdescribed herein. The modules optionally comprising data processinghardware adapted to perform one or more of these steps by havingappropriate machine programming code associated therewith, the modulesfor two or more steps (or portions of two or more steps) beingintegrated into a single processor board or separated into differentprocessor boards in any of a wide variety of integrated and/ordistributed processing architectures. These methods and systems willoften employ a tangible media embodying machine-readable code withinstructions for performing the method steps described above. Suitabletangible media may comprise a memory (including a volatile memory and/ora non-volatile memory), a storage media (such as a magnetic recording ona floppy disk, a hard disk, a tape, or the like; on an optical memorysuch as a CD, a CD-R/W, a CD-ROM, a DVD, or the like; or any otherdigital or analog storage media), or the like.

All patents, patent publications, patent applications, journal articles,books, technical references, and the like discussed in the instantdisclosure are incorporated herein by reference in their entirety forall purposes.

While the above provides a full and complete disclosure of the preferredembodiments of the present invention, various modifications, alternateconstructions and equivalents may be employed as desired. Therefore, theabove description and illustrations should not be construed as limitingthe invention, which can be defined by the claims.

1. A method for determining an ablation treatment for an eye of apatient, comprising: determining an ellipsoid shape corresponding to ananterior corneal surface of the eye, the ellipsoid shape having ananterior portion, a major axis, and an apex, wherein the major axisintersects the anterior portion at the apex; determining a tiltedorientation of the eye when the patient fixates on a target during alaser ablation procedure; and determining the ablation treatment basedon the ellipsoid shape and the tilted orientation.
 2. The method ofclaim 1, wherein the tilted orientation comprises the major axisrotationally offset from an axis of a laser beam path.
 3. The method ofclaim 1, wherein determining the tilted orientation comprises:determining a vertex of the ellipsoid, the vertex corresponding to aforemost point of the anterior corneal surface; and determining anoffset between the apex and the vertex.
 4. The method of claim 1,wherein determining the tilted orientation comprises: obtaining atopography measurement of the anterior corneal surface; and fitting thetopography measurement on the ellipsoid shape to obtain the tiltedorientation.
 5. The method of claim 1, wherein determining the ellipsoidshape comprises determining a keratometry profile of the anteriorcorneal surface.
 6. The method of claim 5, wherein the keratometryprofile comprises a first curvature value, a second curvature value, anda torsional rotational angle.
 7. The method of claim 1, wherein thetilted orientation comprises: a first tilt in a first direction; and asecond tilt in a second direction orthogonal to the first direction. 8.The method of claim 1, further comprising determining one or more of thefollowing: an energy level for a laser treatment device based on theablation treatment; or an ablation time for the laser treatment devicebased on the ablation treatment.
 9. The method of claim 1, furthercomprising determining a wavefront measurement of the eye, wherein theablation treatment is determined based on the ellipsoid shape, thetilted orientation, and the wavefront measurement.
 10. The method ofclaim 1, further comprising adjusting the ablation treatment based on awavefront measurement of the eye.
 11. A method for determining anablation treatment for an eye of a patient, comprising: determining anellipsoid model corresponding to an anterior corneal surface of the eye,the ellipsoid model having an anterior portion, a major axis, and anapex, wherein the major axis intersects the anterior portion at theapex; calculating a nominal ablation pattern for the eye based on theellipsoid model; determining a tilted orientation of the eye when thepatient fixates on a target during a laser ablation procedure, whereindetermining the tilted orientation comprises: determining a surfaceslope of the anterior corneal surface in a first direction extendingradially from the apex; determining a surface slope of the anteriorcorneal surface in a second direction extending radially from the apex,wherein the surface slope in the first direction is steeper than thesurface slope in the second direction; and determining the ablationtreatment by adjusting the nominal ablation pattern based on the surfaceslope in the first direction and the surface slope in the seconddirection.
 12. The method of claim 9, wherein the nominal ablationpattern is based on a surface slope of a non-tilted ellipsoid model. 13.The method of claim 9, wherein determining the nominal ablation patterncomprises calculating a cosine adjustment measure based on a non-tiltedellipsoid model; and wherein determining the ablation pattern comprisesadjusting the cosine adjustment measure based on an adjusted surfaceslope corresponding to the tilted orientation.
 14. The method of claim9, wherein: calculating the nominal ablation pattern comprises applyinga cosine adjustment measure to a wavefront guided treatment plan; andadjusting the nominal ablation pattern comprises adjusting the cosineadjustment measure based on the tilted orientation.
 15. The method ofclaim 9, further comprising: determining a misalignment between an axisof a laser beam and a vertex of the ellipsoid model, the vertexcorresponding to a foremost point of the anterior corneal surface; andadjusting the ablation pattern based on the misalignment.
 16. A computerprogram product for determining an ablation treatment for an eye of apatient, the program product comprising: code for accepting an ellipsoidshape corresponding to an anterior corneal surface of the eye, theellipsoid shape having an anterior portion, a major axis, and an apex,wherein the major axis intersects the anterior portion at the apex; codefor accepting a tilted orientation of the eye, the tilted orientationcorresponding to a laser ablation procedure target fixation of thepatient's eye; code for determining the ablation treatment based on theellipsoid shape and the tilted orientation; and a computer-readablemedium for storing the codes.
 17. A machine-readable medium havingmachine-executable instructions configured to perform a method fordetermining an ablation treatment for an eye of a patient, the methodcomprising: determining an ellipsoid shape corresponding to an anteriorcorneal surface of the eye, the ellipsoid shape having an anteriorportion, a major axis, and an apex, wherein the major axis intersectsthe anterior portion at the apex; determining a tilted orientation ofthe eye when the patient fixates on a target during a laser ablationprocedure; and determining the ablation treatment based on the ellipsoidshape and the tilted orientation.
 18. The machine readable medium ofclaim 17, wherein the tilted orientation comprises the major axisrotationally offset from an axis of a laser beam path.
 19. The machinereadable medium of claim 18, wherein the method further comprises:determining a misalignment between the axis of the laser beam and avertex of the ellipsoid shape, the vertex corresponding to a foremostpoint of the anterior corneal surface; and adjusting the laser ablationpattern based on the misalignment.
 20. The machine readable medium ofclaim 17, wherein the method further comprises determining one or moreof the following: an energy level for a laser treatment device based onthe laser ablation pattern; or an ablation time for the laser treatmentdevice based on the laser ablation pattern.
 21. A system for determiningan ablation treatment for an eye of a patient, comprising: a first inputmodule comprising a tangible medium embodying machine-readable code thatreceives an ellipsoid shape corresponding to an anterior corneal surfaceof the eye, the ellipsoid shape having an anterior portion, a majoraxis, and an apex, wherein the major axis intersects the anteriorportion at the apex; a second input module comprising a tangible mediumembodying machine-readable code that receives a tilted orientation ofthe eye, the tilted orientation corresponding to a laser ablationprocedure target fixation of the patient's eye; and a treatment modulecomprising a tangible medium embodying machine-readable code that thatdetermines the ablation treatment based on the ellipsoid shape and thetilted orientation.
 22. A system for determining an ablation treatmentfor an eye of a patient, comprising: a laser ablation device that emitsa laser beam to ablate at least a portion of the cornea of the patient'seye; and a control device communicatively coupled with the laserablation device and configured to control the laser ablation deviceaccording to the ablation treatment, wherein the ablation treatment isdetermined from a method comprising: determining an ellipsoid shapecorresponding to an anterior corneal surface of the eye, the ellipsoidshape having an anterior portion, a major axis, and an apex, wherein themajor axis intersects the anterior portion at the apex; determining atilted orientation of the eye when the patient fixates on a targetduring a laser ablation procedure; and determining the laser ablationtreatment based on the ellipsoid shape and the tilted orientation. 23.The system of claim 22, wherein the method further comprises:determining a misalignment between an axis of the laser beam and avertex of the ellipsoid shape, the vertex corresponding to a foremostpoint of the anterior corneal surface; and adjusting the laser ablationpattern based on the misalignment.
 24. The system of claim 23, whereinadjusting the laser ablation pattern based on the misalignment comprisesadjusting a cosine measure to account for the misalignment.
 25. Thesystem of claim 22, wherein the method further comprises determining oneor more of the following: an energy level for the laser ablation devicebased on the laser ablation pattern; or an ablation time for the laserablation device based on the laser ablation pattern.